Many structures, including homes, have networks based on coaxial cable (“coax”). The networks are used for distributing video, audio, textual and any other suitable information, and any information related thereto, to network nodes in the structure. The different types of information that may be distributed may be referred to herein as “programming information.”
An organization known as The Multimedia over Coax Alliance (“MoCA™”) provides industry standards (hereinafter referred to as “MoCA”) under which the networks may be operated. MoCA™ provides at its website (www.mocalliance.org) an example of a specification which is hereby incorporated herein by reference in its entirety, for networking of digital video and entertainment information through coaxial cable. The specification has been distributed to an open membership.
Technologies available under the trademark MoCA, other specifications and related technologies (“the existing technologies”) often utilize unused bandwidth available on the coax. For example, coax has been installed in more than 70% of homes in the United States. Some homes have existing coax in one or more primary entertainment consumption locations such as family rooms, media rooms and master bedrooms. The existing technologies allow homeowners to utilize installed coax as a networking system and to deliver entertainment and information programming with high quality of service (“QoS”).
The existing technologies may provide high speed (270 mbps), high QoS, and the innate security of a shielded, wired connection combined with state of the art packet-level encryption. Coax is designed for carrying high bandwidth video. Today, it is regularly used to securely deliver millions of dollars of pay per view and premium video content on a daily basis. Networks based on the existing technologies can be used as a backbone for multiple wireless access points to extend the reach of wireless service in the structure.
Existing technologies provide throughput through the existing coaxial cables to the places where the video devices are located in a structure without affecting other service signals that may be present on the cable. The existing technologies provide a link for digital entertainment, and may act in concert with other wired and wireless networks to extend entertainment throughout the structure.
The existing technologies work with access technologies such as asymmetric digital subscriber lines (“ADSL”), very high speed digital subscriber lines (“VDSL”), and Fiber to the Home (“FTTH”), which provide signals that typically enter the structure on a twisted pair or on an optical fiber, operating in a frequency band from a few hundred kilohertz to 8.5 MHz for ADSL and 12 MHz for VDSL. As services reach such a structure via any type of digital subscriber line (“xDSL”) or FTTH, they may be routed via the existing technologies and the coax to the video devices. Cable functionalities, such as video, voice and Internet access, may be provided to the structure, via coax, by cable operators, and use coax running within the structure to reach individual cable service consuming devices in the structure. Typically, functionalities of the existing technologies run along with cable functionalities, but on different frequencies.
The programming information may be encoded using orthogonal frequency division multiplexing (“OFDM”) or any other suitable encoding scheme. The programming information may be modulated using any suitable modulation scheme, including binary phase shift keying (“BPSK”). The receivers often include bit allocation functions for allocating receiver processing bits to individual OFDM channels. The bit allocation requires an estimate of transmission noise in a signal that communicates the programming information.
Normally, a known signal, such as the Probe 1 signal (defined in the aforementioned MoCA specification) is transmitted to the receiver. The receiver generates a “transmitted” signal by demodulating the signal. The received “transmitted” signal is then, in the physical layer (“PHY”), compared to the known signal, or (in a decision-directed approach) to a “decision” based on the received “transmitted” signal. Any differences between the two signals are defined as “noise”, which may be referred to herein as “transmission noise.”
Demodulation, however, requires carrier channel estimation, whose accuracy is subject to channel noise. Channel noise introduces error into the channel estimation. The error introduces bias into the estimation of transmission noise. The bias can degrade the quality of bit allocation and can therefore degrade signal quality.
For example, the MoCA Probe1 signal payload includes BPSK data generated by a transmitter scrambler. When the same scrambler is used in the receiver, the noise can be estimated by subtracting the known signal from the estimated one, as follows:
                                                        MSE              ^                        k                    =                                                    1                L                            ⁢                                                ∑                                      n                    =                    1                                    L                                ⁢                                                                                                                                                                              x                            ^                                                    k                                                ⁡                                                  (                          n                          )                                                                    -                                                                        x                          k                                                ⁡                                                  (                          n                          )                                                                                                                          2                                                      =                                                            1                  L                                ⁢                                                      ∑                                          i                      =                      1                                        L                                    ⁢                                                                                                                                    w                          k                                                ⁡                                                  (                          n                          )                                                                                                            2                                                              ≈                              σ                                  w                  k                                2                                                    ,                            (                  Eqn          .                                          ⁢          1                )            wherein MSE is mean squared error, which is an estimate of transmission noise, x is signal magnitude, k is carrier index, n is symbol index, L is the number of symbols in a burst, w is noise samples and σwk2 is noise variance. (“^” indicates an estimated value.)
An alternative approach to noise estimation is a data directed approach. In data directed approach, a receiver scrambler is not required. A data directed approach requires the assumption that in the received signal, the signal-to-noise ratio (“SNR”) is favorably high and that the decision is always correct.
For systems using BPSK modulation, in which only the real portion of a signal (i.e., the real portion of the mathematical model of a signal) is used in the decision,{tilde over (x)}k(n)=sgn{Re{{circumflex over (x)}k(n)}},  (Eqn. 2)in which {tilde over (x)}k(n) is the decision on the value of received data. When SNR is favorable, {tilde over (x)}k(n) is approximately equal to the sent data, xk(n).
In both cases described above, the estimation of the “transmitted” signal requires knowledge of the channel transfer function. Since the channel, in general, is unknown, part of the received data sequence is used for channel estimation. Channel estimation based on noisy samples has an error that induces estimation bias in both procedures described above. The bias may be shown by defining new random variable yk(n) as follows:
                                                                                          y                  n                                ⁡                                  (                  n                  )                                            =                                                                                          x                      ^                                        k                                    ⁡                                      (                    n                    )                                                  -                                  sgn                  ⁢                                      {                                          Re                      ⁢                                              {                                                                                                            x                              ^                                                        k                                                    ⁡                                                      (                            n                            )                                                                          }                                                              }                                                                                                                          =                                                                                                                  h                        ^                                            k                      *                                                                                                                                                                    h                            ^                                                    k                                                                                            2                                                        ⁢                                      (                                                                                            h                          k                                                ⁢                                                                              x                            k                                                    ⁡                                                      (                            n                            )                                                                                              +                                                                        v                          k                                                ⁡                                                  (                          n                          )                                                                                      )                                                  -                                  sgn                  ⁢                                      {                                          Re                      ⁢                                              {                                                                                                            x                              ^                                                        k                                                    ⁡                                                      (                            n                            )                                                                          }                                                              }                                                                                                                          =                                                                                          h                      ^                                        k                    *                                                                                                                                                      h                          ^                                                k                                                                                    2                                                  ⁢                                                      v                    k                                    ⁡                                      (                    n                    )                                                                                                                                          =                                                      w                    k                                    ⁡                                      (                    n                    )                                                              ,                                                          (                  Eqn          .                                          ⁢          3                )            wherein h is a channel transfer function, v is channel noise before equalization and “*” indicates a complex conjugate.
If channel estimation does not include error, then The mean of yk(n) is zero. The variance of yk(n) is exactly the noise variance, as follows:
                                                                                          MSE                  ^                                k                            =                                                1                  L                                ⁢                                                      ∑                                          n                      =                      1                                        L                                    ⁢                                                                                                                                                                                              x                              ^                                                        k                                                    ⁡                                                      (                            n                            )                                                                          -                                                  sgn                          ⁢                                                      {                                                          Re                              ⁢                                                              {                                                                                                                                            x                                      ^                                                                        k                                                                    ⁡                                                                      (                                    n                                    )                                                                                                  }                                                                                      }                                                                                                                                      2                                                                                                                          =                                                1                  L                                ⁢                                                      ∑                                          n                      =                      1                                        L                                    ⁢                                                                                                                                    (                                                                                                                    x                                k                                                            ⁡                                                              (                                n                                )                                                                                      +                                                                                          w                                k                                                            ⁡                                                              (                                n                                )                                                                                                              )                                                -                                                  sgn                          ⁢                                                      {                                                          Re                              ⁢                                                              {                                                                                                                                            x                                      ^                                                                        k                                                                    ⁡                                                                      (                                    n                                    )                                                                                                  }                                                                                      }                                                                                                                                      2                                                                                                                          =                                                                    1                    L                                    ⁢                                                            ∑                                              n                        =                        1                                            L                                        ⁢                                                                                                                                                w                            k                                                    ⁡                                                      (                            n                            )                                                                                                                      2                                                                      ≈                                                      σ                                          w                      k                                        2                                    .                                                                                        (                  Eqn          .                                          ⁢          4                )            
Equation 4 shows that the expectation of yk is the noise variance. (The expectation is therefore, in mathematical terms, “unbiased.”) The received signal, however, is accepted for analysis only after it undergoes channel estimation. Since the channel estimation is based on a noisy signal, the estimation includes error. The error may be constant over the burst. The error biases the MSE and, thus the estimate of transmission noise.
The received signal may more accurately be described by the random variable ψ, as follows:
                                                                                          ψ                  k                                ⁡                                  (                  n                  )                                            =                                                                                          x                      ^                                        k                                    ⁡                                      (                    n                    )                                                  -                                  sgn                  ⁢                                      {                                          Re                      ⁢                                              {                                                                                                            x                              ^                                                        k                                                    ⁡                                                      (                            n                            )                                                                          }                                                              }                                                                                                                          =                                                                    (                                                                                            h                          k                          *                                                                                                                                                                h                              k                                                                                                            2                                                                    +                                              e                        k                                                              )                                    ⁢                                      (                                                                                            h                          k                                                ⁢                                                                              x                            k                                                    ⁡                                                      (                            n                            )                                                                                              +                                                                        v                          k                                                ⁡                                                  (                          n                          )                                                                                      )                                                  -                                                      x                    k                                    ⁡                                      (                    n                    )                                                                                                                                          =                                                                            x                      ⁡                                              (                        k                        )                                                              ⁢                                          h                      k                                        ⁢                                          e                      k                                                        +                                                            (                                              1                        +                                                                              h                            k                                                    ⁢                                                      e                            k                                                                                              )                                        ⁢                                                                  w                        k                                            ⁡                                              (                        n                        )                                                                                                        ,                                                          (                  Eqn          .                                          ⁢          5                )            wherein ek is error in the channel estimation for carrier channel k. Based on Eqn. 5:E{ψk}=0, and  (Eqn. 6)E{|ψk|2}=(hkek)+(1+hkek)2σwk2.  (Eqn. 7)The estimation of the noise based on the equalized signal is thus biased and stretched. The bias and stretch may be different for each burst.
It would therefore be desirable to provide apparatus and methods for removing bias from estimates of transmission noise.